Seminars | Mathematical Analysis, Geometry, Numerics and Systems

27th Jan 2026, 16.00-17.00

RA 2231

Prof. Dr. Stefano Stramigioli (University of Twente)

Duality and Covariance Concepts in Numerics.
Even if completely underestimated and sometimes not even thought, duality is at the core of nature and of structure preserving numeric for physical systems. In this talk this statement will be justified and the core ideas of dual fields presented for the study of physics and its structure preserving numerics. Concepts of exterior calculus will be introduced and it will be explained what advantages are achieved using duality in physics and numerics.

15th Dec 2025, 9.30-10.30

RA 3237

Prof. Dr. Catalin Badea
(University of Reading)

Discretisation of Schwarz–Pick Type Inequalities via an Operator-Theoretic Approach.
The general principle of discretisation consists of replacing the supremum norm, or other norms, with evaluations at a finite set of sample points (nodes). This idea goes back to S. N. Bernstein in 1932. In this talk, intended for a general audience, I will discuss appropriate discretisations of the classical Schwarz–Pick inequality, together with the multi-point generalisations due to Beardon–Minda and Baribeau–Rivard–Wegert. The proofs make use of unitary dilations and operator-theoretic methods. All required background will be introduced in the talk.

9th Dec 2025, 9.30-10.30

RA 2334

Dr. Christian Seifert
(TU Hamburg-Harburg)

Controllability and Observability for Systems in Banach spaces.
We review recent results on controllability and observability for linear systems in Banach spaces. In the abstract setting, we will provide sufficient conditions for observability---and thus also controllability. In particular situations of PDEs on $\mathbb{R}^d$, we will also show a necessary condition.

Tuesday 04 December 2024
SPEAKER:  Yvo Boers
Location: RAV 2503
TITLE:  Various Notes on Convergence Results forParticle Filtering: Theory and Practice
ABSTRACT:
We discuss  fundamental results in the field of particle filtering and their implications for practitioners and theoreticians alike . These results were already being used by practitioners in different applications; before they actually had been proven formally in the appropriate theoretical framework.
Some fundamental results, discussed here, are versions of Laws of Large Numbers for Particle Filters(PFs), related to different convergence results for PFs.
Some new results are also presented here. As well as results, that allow the use of empirical expectations for a certain class of unbounded functions and its corresponding convergence to the true expectation, are discussed.
Examples will be provided throughout the presentation.
Speaker: Wouter Edeling
Title: Forward uncertainty quantification in high dimensions
Abstract: Dr Wouter Edeling is a tenured researcher in the Scientific Computing group at CWI. He has a background in aerospace engineering, and obtained a joint-PhD from Delft University of Technology and Arts et Métiers ParisTech in 2015 on the topic of uncertainty quantification for Reynolds Averaged Navier-Stokes (RANS) turbulence closures. He is a recipient of the Center for Turbulence Research Postdoctoral fellowship at Stanford University.
He has worked on physical model error representation in turbulence models, use of advanced Bayesian data analysis such as Bayesian model scenario averaging, and reduced order modelling of unresolved scales.
His current research interest lies at the intersection of machine learning, physical models and uncertainty quantification.
Speaker: Karen Veroy - https://www.tue.nl/en/research/researchers/karen-veroy-grepl
Title: Advances, opportunities, and challenges for parametric model order reduction in digital twins
Abstract: In this talk, we will summarize some recent developments as well as opportunities and challenges in the use of projection-based model order reduction (MOR) for parametrized PDEs in the context of digital twins. In the first part, we consider the development of (a) reduced-order models (ROMs) for multi-scale problems in solid mechanics and (b) sampling strategies for the construction of ROMs in problems with high-dimensional parameters. In the second part, we consider challenges in the use of ROMs digital twins, for example in data assimilation, Bayesian inverse problems, and optimal sensor placement.
Tuesday 05 November 2024 16:00 - 17:15 hrs
SPEAKER: Jan-Frederik Pietschmann https://www.uni-augsburg.de/de/fakultaet/mntf/math/prof/invpde/team/jan-f-pietschmann/
Location: RAV 2504
TITLE:  DATA-DRIVEN GRADIENT FLOWS
ABSTRACT:
We present a framework enabling variational data assimilation for gradient flows in general spaces, metric based on the minimizing movement (or Jordan–Kinderlehrer–Otto) approximation scheme. After discussing stability properties in the most general case, we specialize to the space of probability measures endowed with the Wasserstein distance. This setting covers many non-linear partial differential equations (PDEs), such as the porous-medium equation or general drift–diffusion–aggregation equations, which can be treated by our methods independently of their respective properties (such as finite speed of propagation or blow-up).
We then focus on the numerical implementation using a primal–dual algorithm. This setting covers many non-linear partial differential equations (PDEs), such as the porous-medium equation or general drift–diffusion–aggregation equations, which can be treated by our methods independently
of their respective properties (such as finite speed of propagation or blow-up). We then focus on the numerical implementation using a primal–dual algorithm.
The strength of our approach lies in the fact that, by simply changing the driving functional, a wide range of PDEs can be treated without the need to adopt the numerical scheme.

We conclude by presenting several numerical examples
Tuesday 03 September 2024 16:00 - 17:15 hrs
SPEAKER: Fernando José Henriquez Barraza
Location: RAV 2231
TITLE:  Model of Reduction for Time-Dependent Problems Using the Laplace Transform Joint work with Jan S. Hesthaven (EPFL)
ABSTRACT:
We present a novel, fast solver for the numerical approximation of linear, time-dependent partial differential equations based on model order reduction techniques and the Laplace transform.
We start by applying said transform to the evolution problem, thus yielding a time-independent boundary value problem solely depending on the complex Laplace parameter and the problem's data.
In an offline stage, we carefully sample the Laplace parameter and solve the underlying collection of high-fidelity problems. Next, we apply a proper orthogonal decomposition (POD) to this collection of solutions in order to obtain a basis of reduced order. We project the linear evolution problem onto this basis, and then we solve it using any suitable time-stepping method. We further discussed the applicability of this method to parametric problems. Numerical experiments for parabolic problems and the second-order wave equation portray the performance of the method in terms of accuracy and, in particular, speed-up when compared to standard methods.